63 ideas
| 5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
| 6420 | Only by analysing is progress possible in philosophy [Russell] |
| 6432 | Analysis gives new knowledge, without destroying what we already have [Russell] |
| 1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
| 6437 | The theory of types makes 'Socrates and killing are two' illegitimate [Russell] |
| 6442 | Truth belongs to beliefs, not to propositions and sentences [Russell] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 6436 | I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell] |
| 7528 | Leibniz bases everything on subject/predicate and substance/property propositions [Russell] |
| 6439 | Names are meaningless unless there is an object which they designate [Russell] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 6423 | We tried to define all of pure maths using logical premisses and concepts [Russell] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 6424 | Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell] |
| 6425 | Formalism can't apply numbers to reality, so it is an evasion [Russell] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 6426 | Intuitionism says propositions are only true or false if there is a method of showing it [Russell] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
| 6419 | In 1899-1900 I adopted the philosophy of logical atomism [Russell] |
| 6438 | Complex things can be known, but not simple things [Russell] |
| 6434 | Facts are everything, except simples; they are either relations or qualities [Russell] |
| 6440 | Universals can't just be words, because words themselves are universals [Russell] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 6430 | In epistemology we should emphasis the continuity between animal and human minds [Russell] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 6441 | Pragmatism judges by effects, but I judge truth by causes [Russell] |
| 6431 | Empiricists seem unclear what they mean by 'experience' [Russell] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 6444 | True belief about the time is not knowledge if I luckily observe a stopped clock at the right moment [Russell] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 6433 | Behaviourists struggle to explain memory and imagination, because they won't admit images [Russell] |
| 6443 | Surprise is a criterion of error [Russell] |
| 6427 | Unverifiable propositions about the remote past are still either true or false [Russell] |
| 6435 | You can believe the meaning of a sentence without thinking of the words [Russell] |
| 13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
| 1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
| 404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
| 405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
| 1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |